1. **Stating the problem:** Create and solve three trigonometric function problems. 2. **Problem 1:** Find $\sin(30^\circ)$. - Formula: $\sin(30^\circ) = \frac{1}{2}$. - Explanation: The sine of 30 degrees is a well-known value from the unit circle. 3. **Problem 2:** Solve for $x$ if $\cos(x) = 0$ and $0 \leq x < 2\pi$. - Formula: $\cos(x) = 0$ at $x = \frac{\pi}{2}, \frac{3\pi}{2}$. - Explanation: Cosine equals zero at these points on the unit circle. 4. **Problem 3:** Calculate $\tan(45^\circ)$. - Formula: $\tan(45^\circ) = 1$. - Explanation: Tangent of 45 degrees is the ratio of sine to cosine, both equal, so the result is 1. **Final answers:** - $\sin(30^\circ) = \frac{1}{2}$ - $x = \frac{\pi}{2}, \frac{3\pi}{2}$ for $\cos(x) = 0$ - $\tan(45^\circ) = 1$